My understanding is the Moses went up the Mountain to get the 10 Commandments exactly 3 months after leaving Egypt, and a week or so later went up again for 40 (on g-ds command) days without out telling anyone how long he would be gone. 2 questions
Your question seems to be based on the premise that Moses didn’t tell anyone when he was coming back. That’s a false premise.
The Medieval commentator Rashi, on Exodus 32:1 (the beginning of the Golden Calf story), quotes the Talmud, Shabbas 89a. He says that Moses indeed told them when he was coming back: “At the end of 40 days, I will return during the first six hours.” The problem was a miscommunication - Moses meant forty complete days, and they thought he meant that day on which he ascended should be included.
On the 16th of Tammuz, the day on which the Jews thought he should return, they were concerned - maybe Moses had died up there? Why is he taking so long? Satan took advantage of their confusion and made the world look dark and bleak. The correct response should have been to have faith, wait it out; instead, the people took this as a sign that Moses was dead and resorted to hysteria.
To directly answer your questions, then:
I should highly emphasize here who, exactly, sinned with the Calf. According to the same commentator Rashi as above, it was not all of the Jews who sinned. On Exodus 34:1, regarding G-d telling Moses to carve out a new set of Tablets, Rashi gives a parable to explain why Moses had to do this. A king went overseas, and he left his wife among his maidservants. The maidservants sinned. To prevent rumors that the wife was the one who sinned, a loyal friend of the king’s tore up their marriage document, so that if anyone accuses her of having sinned, the friend can say that they were never married - where’s the marriage document? When the king returned, he saw that it was the maidservants who sinned, and he became appeased. His friend said the king should write a new marriage document; the king told him to prepare the paper, since he was the one who tore it, and the king would write a new document.
Rashi explains the parable succinctly: the king is G-d, the wife is the Jewish people, the friend is Moses, and the maidservants are the Mixed Multitude. The Jews did not sin at the Golden Calf. It was only the Mixed Multitude that sinned. Most of the Jews passed the test - they just failed to stop the Mixed Multitude from sinning.
